NDLI: Maps and Monads for Modal Frames

Content Provider	Springer Nature Link
Author	Goldblatt, Robert
Copyright Year	2006
Abstract	The category-theoretic nature of general frames for modal logic is explored. A new notion of "modal map" between frames is defined, generalizing the usual notion of bounded morphism/p-morphism. The category Fm of all frames and modal maps has reflective subcategories CHFm of compact Hausdorff frames, DFm of descriptive frames, and UEFm of ultrafilter enlargements of frames. All three subcategories are equivalent, and are dual to the category of modal algebras and their homomorphisms.An important example of a modal map that is typically not a bounded morphism is the natural insertion of a frame A into its ultrafilter enlargement EA. This map is used to show that EA is the free compact Hausdorff frame generated by A relative to Fm. The monad E of the resulting adjunction is examined and its Eilenberg-Moore category is shown to be isomorphic to CHFm. A categorical equivalence between the Kleisli category of E and UEFm is defined from a construction that assigns to each frame A a frame A* that is "image-closed" in the sense that every point-image {b : aRb} in A is topologically closed. A* is the unique image-closed frame having the same ultrafilter enlargement as A.These ideas are connected to a category 2U shown by S. K. Thomason to be dual to the category of complete and atomic modal algebras and their homomorphisms. 2U is the full subcategory of the Kleisli category of E based on the Kripke frames.
Starting Page	309
Ending Page	331
Page Count	23
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	83
Issue Number	1-3
e-ISSN	15728730
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	modal map bounded morphism descriptive frame equivalence of categories duality reflective subcategory monad Kleisli category Logic Mathematical Logic and Foundations Computational Linguistics
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Robert goldblatt maps and monads for modal frames.

Maps and monads for modal frames (2004).

Reflective kleisli subcategories of the category of eilenberg-moore algebras for factorization monads.

Modal Provability Foundations for Argumentation Networks

Traced Monads and Hopf Monads

Modal Logics of Reactive Frames

Free Modal Lattices via Priestley Duality

Subdirectly Irreducible Modal Algebras and Initial Frames

On the Modal Logic of Subset and Superset: Tense Logic over Medvedev Frames

Maps and Monads for Modal Frames

Similar Documents

Robert goldblatt maps and monads for modal frames.

Maps and monads for modal frames (2004).

Reflective kleisli subcategories of the category of eilenberg-moore algebras for factorization monads.

Modal Provability Foundations for Argumentation Networks

Traced Monads and Hopf Monads

Modal Logics of Reactive Frames

Free Modal Lattices via Priestley Duality

Subdirectly Irreducible Modal Algebras and Initial Frames

On the Modal Logic of Subset and Superset: Tense Logic over Medvedev Frames

Maps and Monads for Modal Frames